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Interior Point Methods for Linear Optimization

Cornelis Roos Tamás Terlaky Jean-Philiipe Vial

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2005 SpringerLink

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Tipo de recurso:

libros

ISBN impreso

978-0-387-26378-6

ISBN electrónico

978-0-387-26379-3

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer Science+Business Media, Inc. 2005

Cobertura temática

Tabla de contenidos

Introduction

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Pp. 1-11

Duality Theory for Linear Optimization

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Part I - Introduction: Theory and Complexity | Pp. 15-46

A Polynomial Algorithm for the Self—dual Model

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Part I - Introduction: Theory and Complexity | Pp. 47-70

Solving the Canonical Problem

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Part I - Introduction: Theory and Complexity | Pp. 71-83

Preliminaries

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Part II - The Logarithmic Barrier Approach | Pp. 87-105

The Dual Logarithmic Barrier Method

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Part II - The Logarithmic Barrier Approach | Pp. 107-147

The Primal—Dual Logarithmic Barrier Method

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Part II - The Logarithmic Barrier Approach | Pp. 149-212

Initialization

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Part II - The Logarithmic Barrier Approach | Pp. 213-216

Preliminaries

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Part III - The Target-following Approach | Pp. 219-234

The Primal-Dual Newton Method

Cornelis Roos; Tamás Terlaky; Jean-Philiipe Vial

This chapter describes Hume: a functionally-based language for programming with bounded resource usage, including time and space properties. The purpose of the Hume language design is to explore the expressibility/costability spectrum in resource-constrained systems, such as real-time embedded or control systems. It is unusual in being based on a combination of -calculus and finite state machine notions, rather than the more usual propositional logic, or flat finite-state-machine models. The use of a strict, purely functional programming notation allows the construction of a strong cost model for expressions, which can then be embedded into a simple cost model for processes.

In this chapter, we introduce Hume, describe the Hume Abstract Machine implementation, and show how a high-level cost model can be constructed that relates costs from the abstract machine to Hume source programs. We illustrate our approach with an example adapted from the literature: a simple vending machine controller.

Part III - The Target-following Approach | Pp. 235-245